Fortran - I do not understand variable declarations

Question

I need to analize some Fortran code

         subroutine ilocz (a,b,c,n,m)
         real a(n,n),b(n,m),c(n,m)
         do 1 i=1,n
         do 2 j=1,m
         c(i,j)=0
         do 3 k=1,n
   3     c(i,j)=c(i,j)+a(i,k)*b(k,j)
   2     continue
   1     continue
         return
         end

In other place I'm calling this method

call ilocz (a(n11),y(2),a(n12),n,1)

I should refer to ilocz 5 variables - a, b, c, n, m . It is OK. But in first line in ilocz is declaration of arrays. They have te same name as my method arguments.

When i call ilocz i refer 5 real numbers (not arrays) to method. How it is possible? How it works?

Maybe this number is assigned to every array element ( a(11) to a(n,n) , y(2) to b(n,m) , a(n12) to c(n,m) ) or something?

Could someone explain this to me ? Thank you in advance.

Answer 1

Here is the same code, just modernized. As you can see it expects an array of reals for a,b, and c, but FORTRAN is great in that you can treat scalars like arrays

pure subroutine ilocz (a,b,c,n,m)
implicit none
! Arguments
integer, intent(in) :: n,m
real, intent(in)    :: a(n,n),b(n,m)
real, intent(out)   :: c(n,m)
! Local Vars
integer :: i,j,k
do i=1,n
    do j=1,m
    c(i,j)=0
        do k=1,n
          c(i,j)=c(i,j)+a(i,k)*b(k,j)
        end do
    end do
end do
return
end

This we can call as

call ilocz(a(1,1),b,a(2,1),1,1)

which takes the first element of a, the first element of b and writes into the 2nd element of a.

Edit

You can also use the following code:

do i=1,n
    do j=1,m
      c(i,j)=DOT_PRODUCT(a(i,1:n),b(1:n,i)
    end do
end do

or even

c = MATMUL(a,b)

^{see Fortran matrix multiplication performance in different optimization for performance comparisons the different ways to do this}